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User blog:GamesFan2000/Hyper-Nova-Exploding Array Notation (Part 2: Four Entries, Five Entries, and larger linear arrays)
Last time on HNEAN, I made heads explode with my absolutely ridiculous three-entry arrays. Well, it's time to make more heads explode. Four-entry and five-entry arrays are on the house! Four-Entry Arrays {a, b, c, d}: d^^c dimensions of planes. The number of planes in the first dimension is still c^b. Now, does that not look like it will break reality as we know it? (Hint: it will break reality.) {3, 3, 3, 3} will be our guinea pig for this one. Recall that 3^3 is 27. That will be the number of planes in the first dimension. About 3^^3.... tetration is repeated exponentiation. So 3^^3 is actually 3^3^3. That is equal to 3^27. Yikes! 3^27 dimensions! Oh, and what exactly do you think is the answer to the first dimension? If you guessed {3, 3, 3}, you're correct! If you remember how it went in three-entry arrays, you will not be surprised to learn that the number of planes in the second dimension is equal to the answer to the first dimension, the number of layers in the first plane of the second dimension is equal to the answer of the first dimension, and that the answer to the first dimension is used in the first layer of the first plane of the second dimension. Whatever the answer is to the second dimension is applied in the same way to third dimension as the answer to the first was to the second. You will repeat this logic until you solve the 3^27-th dimension. So big...oh wait, there's still five-entry arrays to go through. Five-Entry Arrays In the five-entry arrays, we will enter tetramensional space! You say that it doesn't exist? Sure it does: {a, b, c, d, e}: e^^^d tetramensions of dimensions The amount of dimensions in the first tetramension is d^^c, and the number of planes in the first dimension is c^b. {3, 3, 3, 3, 3} Oh dear. 3^^^3. For the record, that is 3^^(3^27). No words could descibe how many tetramensions are used here. And the answer to the first one is {3, 3, 3, 3}. And that's the number of dimensions in the second tetramension, the number of planes in the first dimension of the second tetramension, the number of layers in the first plane of the first dimension of the second tetramension, and the number that's used in the first layer of the second tetramension. This logic applies to every tetramension, that the answer to the previous tetramension affects the current tetramension. You can literally use that logic for all arrays of all sizes. Beyond Five Entries So, we've seen how to solve up to five entries. There is a pattern to this. For a six-entry array, the number of "pentamensions" is the sixth entry hexated by the fifth entry. The amount of hexamensions in a seven-entry array is the seventh entry heptated by the sixth entry. The logic you see in these arrays don't really change, so you can easily deduce what needs to be done. And that, my friends, is a demonstration of how the linear arrays work...however, this will not be the last that is seen of the notation. Yes, we've got multiple types of arrays in this notation! My next post will be a forray into the 'layered' arrays and how to solve them. See you then! Category:Blog posts